{"id":"940291ba-00bf-41b1-ba0b-034998bc9c41","arxiv_id":"2505.02217","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Clustered competing risks data with event types missing in the main study can be analyzed by weighting or imputing the missing types using classifier probabilities from a training dataset.","lead":"This paper introduces statistical methods for studies where each participant can develop one of several event types, but the exact type is known only for a small training group, not for the main study. The methods let researchers still estimate how a risk factor like tinnitus affects each event type while accounting for clustering, such as two ears within one person.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Weights derived from P(delta|W,Delta=1) ignore the observed event time; under non-proportional cause-specific baseline hazards the weighted score in Equation (6) is biased, and the equal-baseline simulation in Section 3 cannot detect this.","rationale":"The reader's weakest assumption was transportability of the classifier from MUSC to AAA. My concern is more internal: even with perfect transportability and identical training/main mechanisms, the proposed replacement of I(delta=k) with P(delta|W,Delta=1) is generally not the correct conditional expectation because the observed failure time T is informative about the cause when cause-specific baseline hazards differ. The full-data estimating equation (3) is a sum over observed event times; at each event time t, the missing indicator has conditional probability involving lambda_0k(t) / sum_l lambda_0l(t). A classifier fitted on (W, delta) ignores t and therefore yields weights that are valid only under proportional baseline hazards or when W is nearly deterministic. The simulation deliberately uses constant baselines, so it cannot refute this concern; the real application likely violates it because metabolic, sensory, and mixed hearing-loss phenotypes have different age-of-onset patterns. This does not impugn the authors' effort, but it means the central claim requires an additional assumption or a modification of the weights. The proposed simulation test would settle the matter; if it fails, the method needs revision and the real-data hazard ratios should be re-estimated. I therefore recommend keeping the verdict CONDITIONAL, with the condition extended to include time-varying cause-specific baselines.","tokens_in":11375,"tokens_out":11103,"duration_ms":154664,"concrete_test":"Run the Section 3 simulation unchanged except set lambda_01(t)=1 and lambda_02(t)=2t (or use Weibull baselines with different shapes), while continuing to train the multinomial classifier on (W, delta) only, as the paper does. Compare the weighted and imputed estimates of beta_1 and beta_2 with their true values over 1000 replicates. If percent bias exceeds 10% or coverage falls below 90% in any setting, the estimator's validity depends on proportional baseline hazards, and the weights must be time-dependent (e.g., include T as a classifier predictor or use P(delta | W, T, Delta=1)).","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Equation (6) replaces I(delta_ij=k) with P(delta_ij=k | W_ij, Delta_ij=1). But the quantity needed for an unbiased conditional score is E[I(delta_ij=k) | T_ij=t, W_ij, Delta_ij=1, X, v], which under the assumed cause-specific frailty model is proportional to lambda_0k(t) exp(X_ij^T beta_k + v_ik) times the classifier's likelihood contribution from W_ij, not the time-marginal probability P(delta_ij=k | W_ij, Delta_ij=1). Unless all cause-specific baseline hazards are proportional across causes, or W_ij determines delta_ij almost surely, the weighted score is not the conditional expectation of the full-data score and has nonzero expectation at the true beta. The simulation in Section 3 sets lambda_0k(t)=1 for all k, so this bias mechanism is absent from every simulation setting; moreover, the training and main data are generated from the same mechanism, so the transportability condition is also baked in. The real-data analysis in Section 4 uses metabolic, sensory, and metabolic+sensory hearing-loss phenotypes whose age-at-onset hazards are likely to differ, so the hazard ratios in Tables 2-3 may be biased. The imputed estimator in Section 2.3 inherits the same problem because the hard assignments also ignore event time.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript develops weighted and imputed estimating equations for cause-specific hazard ratios in clustered competing risks data when event types are missing in the main study but are available in a training dataset. In the weighted approach, the unobserved indicators I(δij=k) in the penalized partial likelihood score are replaced by classifier-based probabilities P(δij=k | W, Δ=1); in the imputed approach, event types are replaced by the argmax of those predicted probabilities. The authors derive a sandwich-type variance estimator and also recommend the inverse-Hessian estimator from the coxme package, evaluate finite-sample performance in simulations with constant and equal cause-specific baseline hazards, and apply the methods to estimate associations between tinnitus and metabolic, sensory, and metabolic+sensory hearing loss in the CHEARS AAA cohort using a classifier trained on the MUSC database.","tokens_in":11583,"tokens_out":9298,"duration_ms":125784,"significance":"If the proposed estimators are valid, the paper fills a practical gap: clustered competing risks data with event types available only in an auxiliary training set are common in epidemiologic studies, and the proposed use of existing software (coxme) would make the methods accessible. The real-data application and the explicit discussion of the event-time measurement error limitation are welcome. However, the central estimator is not shown to be an unbiased estimating equation under the stated model unless strong extra conditions hold; the simulation design uses equal constant baseline hazards and generates training and main data from the same mechanism, so the reported bias and coverage results do not establish general validity. The significance of the contribution is therefore conditional on a substantial reworking of the weighting scheme and the simulation evidence.","major_comments":[{"comment":"The weighted estimating equation in Eq. (6) replaces I(δij=k) with P(δij=k | Wij, Δij=1), but the quantity needed for an unbiased conditional score is P(δij=k | Tij, Xij, vi, Wij, Δij=1). Under the assumed cause-specific frailty model, this conditional probability is proportional to λ0k(Tij) exp(Xij^T βk + vik) times the classifier's contribution from Wij, divided by the sum over causes. It therefore depends on the event time through the baseline hazard ratio λ0k(Tij)/λ0l(Tij) and on the covariates and frailty through exp{Xij^T(βk-βl) + vik - vil}. Equation (6) uses a time-marginal probability that conditions only on W and Δ, so the weighted score generally has nonzero expectation at the true β. The imputed estimator in Section 2.3 inherits the same problem because the hard assignments also ignore event time, covariates, and frailty. The simulation in Section 3 sets λ0k(t)=1 for all k and generates training and main data from the same mechanism, so this bias mechanism is absent from every simulation setting. The real-data analysis in Section 4 uses hearing-loss phenotypes whose age-at-onset hazards are likely to differ, so the cause-specific hazard ratios in Tables 2–3 may be biased. The authors should either replace the weights with estimates of the conditional probability given T, X, and v, or provide a formal asymptotic justification with clearly stated conditions under which Eq. (6) is an unbiased estimating equation.","section":"Section 2.2, Eq. (6); Section 2.3; Section 3; Tables 2–3"},{"comment":"There is a contradiction between the method statement and the application. Section 2.2 explicitly says the classification model is fitted among participants that have experienced the events (Δij=1), but the real-data analysis builds the classifier on all 338 MUSC ears, 11% of which are labelled 'older-normal (i.e. without hearing loss)'. Those older-normal ears are censored observations (Δ=0), not observed event types, so including them as a fourth class means the classifier does not estimate P(δ=k | W, Δ=1); the predicted probabilities for the three hearing-loss types are not the conditional event-type probabilities required by Eq. (6). This label contamination can bias the hazard ratio estimates in Tables 2 and 3. The analysis should either restrict the training sample to ears with hearing loss and treat older-normal ears as censored, or explicitly model the conditional probability of event type given that an event occurred.","section":"Section 4, MUSC training data; Section 2.2"},{"comment":"The variance estimator in Eq. (7) treats the estimated probabilities P(δ|W) as known, and the paper cites Lok (2021) to argue that ignoring this estimation is conservative. In the present setting, the probabilities are estimated from a training sample that is separate from the main study, and ignoring that estimation step generally understates the variability of the estimating equation rather than overstating it. The coverage probabilities in Table 1 are close to nominal in most cells, but several cells fall to 0.92–0.93 (e.g., (1000,50), (log(1.5), log(1.75)), γ=2.5, weighted β2; (1000,100), (log(1.5), log(1.75)), γ=2.5, imputed β2). The authors should either derive a variance estimator that accounts for the estimated classifier or empirically evaluate the magnitude of the undercoverage by reporting the coverage when training samples are redrawn across replicates, which is already the case in the simulation but is not reflected in the inference.","section":"Section 2.2, Eq. (7); Table 1"},{"comment":"The simulation design bakes in transportability of the classifier: the training and main data are generated from the same data-generating mechanism, and the classifier (multinomial logistic regression on W) is correctly specified for the conditional distribution of W given δ. The real-data application instead requires transporting a classifier from the MUSC database to the CHEARS AAA cohort, where the relationship between audiometric thresholds and hearing-loss phenotypes, or the phenotype definitions themselves, may differ. A simulation that trains the classifier under one mechanism and applies it to main-study data generated under a different mechanism (e.g., different W|δ distributions or different cause-specific baseline hazards) is needed to assess the method's robustness. Without such a sensitivity analysis, the real-data results in Tables 2 and 3 cannot be interpreted as reliable estimates of the cause-specific hazard ratios.","section":"Section 3; Section 2.2"}],"minor_comments":[{"comment":"The text says the regression parameters are chosen among {(log(1.25), log(1.5)), (log(1.5), log(1.75)), (log(1.5), log(1.75))}, but the second and third pairs are identical; presumably one of them should be (log(1.5), log(1.5)) as used in Table 1.","section":"Section 3"},{"comment":"The confidence intervals for the sensory hearing loss associations are extremely wide (for example, 0.55–4.89 in the QDA-weighted row), so the statement that the associations 'are not substantially different' is not well supported; reporting p-values for the difference or a joint test would be more informative.","section":"Section 4, Tables 2–3"},{"comment":"The information matrix formulas use tij in the denominators while the main text uses Tij; the notation should be made consistent.","section":"Appendix"},{"comment":"The figure shows four groups including older-normal, but the main-study analysis is for three hearing-loss phenotypes; the authors should clarify how predicted older-normal probabilities are handled for participants with hearing loss, since the method in Section 2.2 conditions on Δ=1.","section":"Figure 1 and Section 4"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a practically important problem and the proposed computational strategy via coxme is attractive, but the core estimator is not a conditional score under the stated model, and the simulation design is too favorable to reveal the resulting bias. The contradiction between the method's conditioning requirement and the MUSC training data in the application is also concerning. I believe the approach is salvageable: the weights should condition on event time and covariates (or the authors should provide a rigorous asymptotic justification under explicit conditions), the variance estimator should account for the estimated classifier, and the simulations should include non-proportional baseline hazards and distributional shifts between training and main data. I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper is worth a look if you work on competing risks with missing causes. It extends cause-specific proportional hazards frailty models to the case where event types are missing in the main study but available in a training set, using weighted or imputed estimating equations. That combination is new in the cited literature, and the implementation via coxme is a practical plus.\n\nWhat it does well: clear setup, standard penalized partial likelihood machinery, simulations show low bias and good coverage when baselines are equal and the classifier is accurate. They give analytical variance formulas. The real application to hearing loss is interesting, and the stacking ensemble is a thoughtful touch.\n\nThe biggest soft spot is in Equation (6). The weight is P(delta=k | W, Delta=1), marginal over event time. For the score to be unbiased at the true beta, you need the conditional expectation of I(delta=k) given the full data, including T. That conditional expectation depends on the cause-specific baseline hazards at t. If the lambda_0k(t) are not proportional across causes, the time-marginal weight is misspecified and the estimating equation has nonzero mean. The simulation sets lambda_0k(t)=1 for all k, so the bias mechanism never appears. That is central, not minor.\n\nSecond, the variance estimator deliberately ignores uncertainty in the estimated event probabilities. With training samples of 50 or 100 in simulations and 338 in the application, confidence intervals could be anti-conservative. The paper actually states it ignores this, so the authors are candid, but the consequence is understated.\n\nThird, the real-data analysis transports a classifier from MUSC to the AAA cohort. The paper notes the training set is external but does not discuss possible differences in phenotype definitions or population. The simulation bakes in transportability by generating training and main data from the same mechanism.\n\nThe authors do flag the measurement error assumption and the ignored probability estimation, so they are engaged. They just miss the time-dependence issue, which is the more serious one.\n\nBottom line: the paper addresses a real problem and the methods are coherent, but the weighted estimator needs a correction or at least a stated condition of proportional cause-specific baseline hazards, and the real-data conclusions should be framed as conditional on that plus transportability. I would send it to a serious referee, but I would ask the referee to focus on the time-dependence of the weights and to require simulations with non-proportional baselines.","headline":"Useful extension of cause-specific frailty models to missing event types, but the weights ignore event time; under non-proportional baselines the estimators can be biased, and the simulations don't cover that.","tokens_in":12128,"tokens_out":2343,"would_cite":true,"duration_ms":33132,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62N01","62N02","62H30","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Cause-specific hazard ratios can be estimated from clustered competing-risks data with missing event types by substituting classifier probabilities for the unobserved event-type indicators in the penalized partial likelihood.","keywords":["competing risks","cause-specific hazards","frailty models","penalized partial likelihood","missing event types","weighted estimating equations","imputation","hearing loss"],"falsifier":"Simulate a main study and a training dataset drawn from different class-conditional distributions (for example, shift the mean audiometric thresholds for a given hearing-loss phenotype by several decibels between the two samples), fit the weighted estimator, and check whether the percent bias of the cause-specific log-hazard ratios exceeds the roughly 5% level reported in the paper; if so, the transportability assumption is violated in a way the current simulations do not capture.","tokens_in":11123,"feed_emoji":"📊","tokens_out":7979,"duration_ms":84523,"temperature":0.7,"pith_summary":"Epidemiological studies often know when someone dies or develops a condition but not which of several competing causes was responsible. This paper develops methods for clustered survival data—for example, two ears within a person—where the event type is missing in the main study but available in a small training set together with predictive covariates. The authors propose two approaches: a weighted penalized partial likelihood that substitutes the estimated probability of each event type for the unknown indicator, and an imputation approach that assigns the most probable type. Simulations show both estimators usually have bias below 5% and confidence intervals with coverage close to the nominal 95% when the classifier is accurate. An application to hearing-loss data finds a significant association between tinnitus and metabolic+sensory hearing loss, but not the other two phenotypes.","feed_headline":"Classifier probabilities fill in missing competing-risk event types","feed_subtitle":"Weighted and imputed estimators keep bias below 5 percent with near-nominal coverage in clustered survival data.","key_machinery":"The load-bearing object is the penalized partial likelihood (PPLL) for the cause-specific proportional hazards frailty model, where each cluster (a participant) carries correlated random effects across the $K$ event types. In the complete-data score equation, the factor $I(\\delta_{ij}=k)$ multiplies the 'observed-minus-expected' covariate contribution of each failed unit. The paper's central move is to condition on the observed censoring indicator $\\Delta_{ij}=1$ and the predictive covariates $W_{ij}$, replacing $I(\\delta_{ij}=k)$ with $P(\\delta_{ij}=k\\mid W_{ij},\\Delta_{ij}=1)$ in the weighted approach, or with $I(\\hat\\delta_{ij}=k)$ in the imputed approach. This substitution turns the PPLL into a weighted partial likelihood that can be maximized with standard penalized survival software.","core_discovery":"The paper's central claim is that the score equations of the penalized partial likelihood remain valid when each unknown event-type indicator $I(\\delta_{ij}=k)$ is replaced by the conditional probability $P(\\delta_{ij}=k\\mid W_{ij},\\Delta_{ij}=1)$ estimated from a training set. The resulting weighted estimating equations yield cause-specific hazard ratio estimates whose percent biases in simulations are generally under 5% and whose 95% confidence intervals have coverage close to nominal. A hard-imputation alternative, which assigns $\\hat\\delta_{ij}=\\arg\\max_k \\hat P(\\delta_{ij}=k)$, performs comparably and is sometimes less biased for large effects, while the weighted version is usually more efficient. The paper further claims that analytical variance estimators—sandwich and inverse Hessian—provide usable inference, and that the weighted model can be fitted with existing software through data duplication.","pith_inferences":["The variance formulas ignore that the event-type probabilities are themselves estimated; with small training samples, standard errors may be understated, and a bootstrap or delta-method correction would propagate that uncertainty.","The simulations train and apply the classifier under the same data-generating mechanism, so the transportability assumption is not stress-tested; a distribution-shift simulation would quantify how miscalibration translates into bias.","The weighted estimator is a form of inverse-probability weighting, suggesting a doubly robust extension that remains consistent if either the survival model or the classification model is misspecified.","The paper notes its event-time measurement-error assumption may fail in self-reported hearing loss data; correcting for both outcome and event-time error is a natural next step."],"forward_implications":["Careful analysts can now estimate cause-specific hazard ratios in cohort studies where event types are only ascertained in a validation sub-study, without discarding the main cohort.","The derived variance estimators make the method usable for inference, not just point estimation, in the settings the simulations cover.","Because the weighted model can be fit through data duplication in existing software packages, the approach is implementable with tools already used in practice.","In the hearing-loss example, the method yields a stable, statistically significant elevated hazard ratio for tinnitus with metabolic+sensory hearing loss across five classification models."],"supporting_citations":[{"why":"Defines the cause-specific proportional hazards model that the paper extends to clustered frailty data.","marker":"Prentice et al. (1978)"},{"why":"Introduces penalized partial likelihood for frailty models, the estimation target the paper modifies for missing event types.","marker":"Ripatti and Palmgren (2000)"},{"why":"Applies PPLL to competing risks clustered data and supplies the sandwich variance approach underlying Equation (7).","marker":"Dharmarajan et al. (2018)"},{"why":"Derives the PPLL approximation and the estimating equations for clustered survival data used as the starting point.","marker":"Wang et al. (2020)"},{"why":"Prior method for missing failure types under proportional baseline hazards, which this paper generalizes to clustered frailty models.","marker":"Goetghebeur and Ryan (1995)"},{"why":"Multiple imputation approach for missing cause of failure; the paper's imputed approach is an alternative imputation strategy.","marker":"Lu and Tsiatis (2001)"},{"why":"Provides the MUSC training dataset of ears with audiometric thresholds and expert hearing-loss phenotypes used to train the classifiers.","marker":"Dubno et al. (2013)"},{"why":"Basis for using penalized survival software and inverse-Hessian variance estimates.","marker":"Therneau et al. (2003)"}],"fun_headline_variants":["Missing event types? Train a classifier to weight competing risks","Impute or weight event types using training data in clustered risks","Low-bias estimates for clustered risks with missing cause types","Probability weights from training set fill missing event types"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classifier that supplies the event-type probabilities must be transportable: the relationship between the covariates $W_{ij}$ and the event types in the training dataset must match the relationship in the main study, or the weights and imputed types are systematically wrong and the hazard ratios are biased.","fun_headline_variants_meta":{"raw":{"variants":["Missing event types? Train a classifier to weight competing risks","Impute or weight event types using training data in clustered risks","Low-bias estimates for clustered risks with missing cause types","Probability weights from training set fill missing event types"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00184,"raw_usage":{"total_tokens":7201,"prompt_tokens":880,"completion_tokens":6321,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":496,"completion_tokens_details":{"reasoning_tokens":6255}},"tokens_in":496,"tokens_out":6321,"duration_ms":46925,"temperature":1.0,"reasoning_tokens":6255,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:58:33.609914+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a main study and a training dataset drawn from different class-conditional distributions (for example, shift the mean audiometric thresholds for a given hearing-loss phenotype by several decibels between the two samples), fit the weighted estimator, and check whether the percent bias of the cause-specific log-hazard ratios exceeds the roughly 5% level reported in the paper; if so, the transportability assumption is violated in a way the current simulations do not capture.","supporting_citations":[],"review_version":1}